For a 2x2 table from a matched pair experiment, we examine McNemar tests with and without continuity correction, Minimum chi-square test by Bhapkar and likelihood ratio test, with respect to null and non-null exact distributional properties. McNemar test without continuity correction achieves the best approximation to the nominal significance level. Formulae for power calculation and required number of subjects are also discussed.
keywords: Matched pair experiment, McNemar test, Type one error rate, Power formula, Sample size calculation, Unconditional exact distributionConsider the ranked set sampling which is useful to estimate the population mean when the order of a sample of small size can be found without measurements or with rough methods. Consider m sets of elements each set having size m. All elements of each set are ranked but only one is selected and quantified. Continue the process n times and the average of the quantified elements is adopted as the point estimator. In this paper we shall try to construct interval estimators of the population mean. In order to construct interval estimators, we derive estimators of the variance of the average and standardize the average. Normal approximation and t-approximations with predetermined or adjusted degrees of freedom are considered. We find that the t-approximations with adjusted degrees of freedom are effective except for heavily skewed distributions.
keywords: Ranked set sampling, Population mean, Interval Estimation, t-approximation, Normal approximation
In this paper, a method for classifying items and judges from
ranked observations by using the rank graph is proposed.
The rank graph was proposed originally as a descriptive one in which
an average rank and a degree of concordance of ranks assigned to
each item are represented by the vector called item vector.
As the distribution of an item vector is asymptotically approximated
by a 2-dimensional normal distribution,
we can obtain an elliptic confidence region of the item vector.
According to whether confidence regions of the items
overlap or not each other, the items can be classified.
On the other hand, the judges may rank items such that
there is little difference in quality between
the items belonging to the same group.
After classifying the items,
ranking of the items reduces to ranking of the groups of the items.
Thus, the judges are classified with the patterns
that the judges order the groups.
It will be shown that it is possible to classify the items and
the judges hierarchically according to the confidence coefficient.
In this paper, we propose a framework based on ``Frame Theory''
for data analysis supporting system to construct the set of the
knowledge for data analyses.
There is some research to which the technique of knowledge processing
to data analysis is applied. In the field of knowledge processing,
a knowledge base and an inference function are to be independent for
flexibility of a system.
Most reports about the application, however, may not tell us that both
parts are separated clearly.
In this paper, we compare some methods about knowledge representation
shown in the previous works for data analysis supporting systems and
show that ``Frame Theory'' is the most available when we focus on
the supporting function to select appropriate statistical procedures.
We also offer how to implement the knowledge of data analysis on the
framework and show two examples about supporting functions based on
our knowledge base and the independence of the knowledge base and the
inference functions through these examples.
Scientific Visualization, the application of computer graphics techniques
to produce pictures of complex volume image and physical phenomenon,
is emerging as a very powerful means of enabling scientists and
researchers to interpret their data. The theories of image generation
have been investigated over 20 years, however, most conventional computer
graphic techniques are optimized for well organized data base elements such
as polygon. In most application of scientific visualization, source
data to be visualized are pre-organized data set such as volume metric data
and many new techniques have been developed last 10 years. These techniques
are generalized to volume rendering method.
In this article, I would like to introduce volume ray tracing methods
to visualize three dimensional and four dimensional volume
metric data. The results of visualization from medical images are shown.